Scalar product used for length?

[phospho]

I got asked how the scalar product can be used to find the length of a vector? Could someone please explain

 

[UltrafastPED]

Do you mean vector product, also called the dot product?

V°V = |V|^2.

Or do you mean the triple scalar product:

|A°BxC|= volume of the parallelepiped with three sides defined by A,B,C.


If it is the triple scalar product you will need more information to obtain a vectors length - but the dot product provides it immediately.

 

[FeDeX_LaTeX]

Do you mean vector product, also called the dot product?

V°V = |V|^2.

Or do you mean the triple scalar product:

|A°BxC|= volume of the parallelepiped with three sides defined by A,B,C.If it is the triple scalar product you will need more information to obtain a vectors length - but the dot product provides it immediately.

To my knowledge, the vector product and the dot product are never given the same meaning. The vector product yields a vector quantity; the dot product yields a scalar quantity.

I'm not sure how one could use the scalar product to find the length of an arbitrary vector -- it seems like a redundant question to me. Do you know how to find the magnitude of a vector?

 

[UltrafastPED]

To my knowledge, the vector product and the dot product are never given the same meaning. The vector product yields a vector quantity; the dot product yields a scalar quantity.

There are many vector products: http://mathworld.wolfram.com/VectorMultiplication.html

Two of those listed above result in a scalar. I was trying to determine which one he was referring to; the OPs language was ambiguous.

The vector inner product (dot product) is the obvious method.

But the original requestor has disappeared ... so the problem is dead.